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Centered Partition Processes: Informative Priors for Clustering (with Discussion).

Sally Paganin1, Amy H Herring2, Andrew F Olshan3

  • 1Department of Environmental Science, Policy, and Management, University of California, Berkeley.

Bayesian Analysis
|August 12, 2022
PubMed
Summary

This study introduces a Centered Partition (CP) process for Bayesian clustering, incorporating expert prior knowledge. The method favors partitions close to initial expert groupings, enhancing clustering accuracy in applications like birth defect analysis.

Keywords:
Bayesian clusteringBayesian nonparametricsDirichlet Processcentered processexchangeable probability partition functionmixture modelproduct partition model

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Area of Science:

  • Statistics
  • Bayesian Inference
  • Computational Statistics

Background:

  • Bayesian clustering commonly uses Exchangeable Partition Probability Functions (EPPFs), often assuming exchangeability.
  • Existing methods offer limited flexibility for incorporating specific prior knowledge into partition structures.
  • Expert-defined initial clusterings are valuable but challenging to integrate into standard Bayesian models.

Purpose of the Study:

  • To develop a general Bayesian approach for clustering that explicitly incorporates prior knowledge on partitions.
  • To introduce the Centered Partition (CP) process, modifying EPPFs to favor partitions near a specified initial structure.
  • To demonstrate the utility of the CP process in epidemiological applications, specifically clustering birth defects.

Main Methods:

  • Proposed the Centered Partition (CP) process as a modification of Exchangeable Partition Probability Functions (EPPFs).
  • Developed a general algorithm for posterior computation within the CP framework.
  • Utilized simulation studies and a real-world epidemiological dataset for methodology validation.

Main Results:

  • The CP process effectively incorporates expert-defined initial clusterings into Bayesian partition models.
  • The developed algorithm enables efficient posterior computation for the CP prior.
  • The methodology showed practical applicability in clustering birth defects based on prior expert knowledge.

Conclusions:

  • The Centered Partition (CP) process provides a flexible framework for Bayesian clustering with prior knowledge.
  • This approach enhances the integration of domain expertise into statistical modeling for partition-based problems.
  • The CP process offers a valuable tool for applications requiring informed clustering, such as epidemiological studies.